
174 Exposure-Response Modeling: Methods and Practical Implementation
model of y
i1
. In most s ituations in ER modeling with fixed (and often small)
J, the LS estimates are inconsistent when n → ∞. When treating u
i
as an
random effect, however, the MLEs for all model parameters are consistent,
hence it is a practical choice. How to treat y
i0
s in the model is sometimes an
important issue. See Hsiao (2003) for details.
When u
i
is considered random, this model can be written as a marginal
model
y
ij
= ρ
j
y
i0
+ β
j
X
j
′
=1
ρ
j−j
′
c
ij
′
+ ε
∗
ij
(6.36)
as a function of whole exposure history. T he first term represents the marginal
time profile of the sys tem dynamic without the ...